PHOENIX — The Giants never gave Jerry Reese a public ultimatum — “Fix this or you’re out!” — but when the team parted ways with Tom Coughlin and co-owner John Mara said it would be up to Reese to get the Giants back on track after four seasons without making the playoffs, it was pretty clear what the repercussions might have been had the team fallen short again in 2016.

The Giants did not. Reese brought in three key defensive free agents in Olivier Vernon, Janoris Jenkins and Damon Harrison, spending $200 million on the overhaul. And it likely saved Reese’s job.

“There was a lot of heat on Jerry,” Giants co-owner Steve Tisch acknowledged yesterday at the NFL’s annual meeting in Arizona. “John Mara, my partner, made it very clear to Jerry: ‘We’re watching you and we have very high expectations and it’s your time to deliver.’ The moves he made last season, clearly in retrospect, were hugely significant and really changed the whole defense of the team. I’m thrilled that Jerry accepted the challenge, acknowledged what he had to do, and he did it. That doesn’t happen every time. It doesn’t happen really that often.”

It did this time.

“I’m thrilled,” Tisch said of the overall state of the team. “. . . Jerry is filling in the holes really, really nicely [this offseason] . . . Jerry has done a fantastic job.”

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Did Pats fear Giants?

Tisch said he is very happy with how 2016 played out, but there still are a few regrets.

“Would I have liked to have gone deeper into the playoffs? Of course,” he said. “Would I have liked to end up in Houston? Absolutely. Especially because [Patriots owner] Bob Kraft after the Super Bowl told me: ‘You would have beat us.’ That was a nice compliment.”

The Patriots, of course, won their fifth Lombardi Trophy with an epic comeback in Super Bowl LI against the Falcons. Their only two Super Bowl losses during the Tom Brady-Bill Belichick era have come at the hands of the Giants, so it makes sense that the Patriots and Kraft might be spooked by the prospect of having to face them and Eli Manning for another championship.

Giants videos

Unless, of course, Tisch heard something different from what Kraft was saying. Asked by Newsday about Tisch’s anecdote, Kraft told a different story, saying that he never said the Giants would have beaten the Patriots in that game this year.

“I said we lost two right at the end, and if I had to lose them to anyone, because it’s the Giants, [that was fine],” Kraft said. “That was the background.”

End zone

There is no indication that the Giants are close to landing former Jets center Nick Mangold, though they likely reached out to him as part of their offseason work. “We look into everything,” Reese said at the NFL meeting . . . Tisch said he and the Giants remain optimistic that they eventually will land defensive tackle Johnathan Hankins, the only one of the 11 defensive starters from last year who still is unsigned by the team. Tisch said the Giants’ offer remains on the table and that the team will be patient.

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Are the Giants looking for an heir to Manning this offseason? “I think it’s certainly at the back of everybody’s mind,” Tisch said. “There is no urgency, there is no panic. But if you are a responsible owner, responsible GM, you have to start thinking about it.” . . . Wide receiver Brandon Marshall said signing with the Giants was “absolutely” a good move for former Jets teammate Geno Smith. “I’m excited to see him continue to grow,” Marshall said. Smith will compete with Josh Johnson to be Manning’s backup . . . Marshall said he will participate in Manning’s annual get-together with Giants wide receivers at Duke in early April before the start of the official offseason program on April 18.